When used as a clock in a circuit: microprocessor.
Using an oscilloscope should I view the waveform by measuring across the crystal or with respect to ground?

 

Best answer is neither: your scope capacitance is going to change the circuit so what your measuring is different from what your circuit really is.

If you measure across the cap you need to use two probes and subtract the inputs as generally you do not want to ground one end of the crystal.

If you must measure the crystal measure each end to ground in two measurements